Solve for $x$ and $y$ using elimination. ${-3x+2y = 1}$ ${-4x-6y = -68}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ ${-9x+6y = 3}$ $-4x-6y = -68$ Add the top and bottom equations together. $-13x = -65$ $\dfrac{-13x}{{-13}} = \dfrac{-65}{{-13}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-3x+2y = 1}\thinspace$ to find $y$ ${-3}{(5)}{ + 2y = 1}$ $-15+2y = 1$ $-15{+15} + 2y = 1{+15}$ $2y = 16$ $\dfrac{2y}{{2}} = \dfrac{16}{{2}}$ ${y = 8}$ You can also plug ${x = 5}$ into $\thinspace {-4x-6y = -68}\thinspace$ and get the same answer for $y$ : ${-4}{(5)}{ - 6y = -68}$ ${y = 8}$